I would like to use WEAP to model the water allocation planing in one of the watershed here as part of my thesis. I'm calibrating the model in 4 streamgauges and I'm surprised to see no flow in the catchment inflow node of my river while the streamgage have flow.

I don't know what data you've entered into your river, but the data in the streamflow gauges don't interact with the model - they are there for comparison purposes. If you don't have flow in your river, you probably have not given it a source of water, either by entering the headflow data in the river itself, or by creating catchments. Then you can compared the modeled data to your historic streamflow gauge data to calibrate the model.

The reservoirs have a default demand priority of 99. If there are any other demands in the system (such as a city, agricultural site, or instream flow requirement), those had a default demand priority of 1.

This means that the reservoir(s) will only fill when all demands downstream are met: they cannot withhold water from demand sites with higher demand priorities. If your system has more demand than supply downstream of the reservoir, the reservoir will never retain water. Instead it will pass it downstream so the other demand sites can meet their demand.

You can look at this in 2 ways in the results section. Navigate to Demand/Unmet Demand, and see if your downstream demand sites have deficits, and when. This is when the reservoir will not retain water. You can also look at Supply and Resources/Reservoir/Storage Volume, to see if (and when) the reservoirs are getting water. If there are no periods of complete coverage for your downstream demand sites, there are probably no periods when your reservoir is getting supply. Alternatively, maybe it is storing some water, and then giving it away immediately to meet the demands downstream. Let me know if that is that case, and if you don't want that.

Please help me -- I have two reservoirs in my model application and they should be filled every year and satisfye demand (mainly irrigation and Drinking water).

The first one is filled every year except in drought years. It delivers water to demand sites but it still retain water while There is high unmet demand in these irrigated perimeters.

The second one, the storage is equal to 0 in all years while it should deliver water to two irrigated perimeters. There is high unmet demand there.

There is something wrong. Maybe the reservoir is not receiving much water for deliveration but this should be the case only for drought years. Also, when I run reference scenario for the 2030 horizon, the volume is 0.

Is your irrigation downstream of the reservoir? What is its demand priority?

If there is unmet demand downstream, the reservoir will not retain any water. It will let the demand site take the water. Reservoirs are effective in situations where there is too much water sometimes (for example, in the winter) and not enough water at other times (like the summer). Reservoirs can collect water during the wet times to release them during the dry times. However, if your agriculture demands water all year and there is always insufficient water, there is never a good time for the reservoir to collect water.

Have you entered "Monthly variation" information for your agriculture sites? There's a good example of this in the WEAP tutorial (in the first exercise, WEAP in One Hour). That way you can make sure that your annual patterns of agricultural demand reflect the temporal demands in the system.

Is your irrigation downstream of the reservoir? What is its demand priority?

In the absence of other constraints***(see below), if there is unmet demand downstream, the reservoir will not retain any water. It will let the demand site take the water. Reservoirs are effective in situations where there is too much water sometimes (for example, in the winter) and not enough water at other times (like the summer). Reservoirs can collect water during the wet times to release them during the dry times. However, if your agriculture site demands water all year and there is always insufficient water, there is never a good time for the reservoir to collect water.

Have you entered "Monthly variation" information for your agriculture sites? There's a good example of this in the WEAP tutorial (in the first exercise, WEAP in One Hour). That way you can make sure that your annual patterns of agricultural demand reflect the temporal demands in the system.

***Other constraints that can hinder the reservoir from releasing water: There are several constraints you add in WEAP that would affect the behavior of the reservoir. Here are some examples:
1) Transmission to the demand sites is limited: if you constrain your transmission link, the reservoir will only release as much water as can be supplied in the transmission link, rather than the total quantity of demand.
2) You have entered information about an inactive zone in your reservoir. That water, by definition, cannot be accessed.
3) You have entered information about a buffer zone in your reservoir, which might limit how much can be released in a single timestep.
4) You have entered information the reservoirs maximum hydraulic outflow.